Statement-1: The point \) is the mirror image of the point \) in the plane Statement-2: The plane bisects the line segment joining \) and \)

Statement-1 is true and Statement-2 is true: Statement-2 is not the correct explanation for Statement-1

Maths · Coordinates of a point in space, the distance between two points, section formula

Statement-1: The point \) is the mirror image of the point \) in the plane State

Statement-1: The point \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) \) is the mirror image of the point \( B(1,3,4) \) in the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) Statement-2: The plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) bisects the line segment joining \( \boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) \) and \( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)

A. Statement-1 is true and Statement-2 is true: Statement-2 is not the correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is false
C. Statement-1 is false, Statement-2 is true
D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-

Step-by-step solution

The midpoint of A(3,1,6) and B(1,3,4) is (2,2,5), which lies on the plane x - y + z = 5. Also, the direction vector of AB is (2,-2,2) which is parallel to the normal vector (1,-1,1) of the plane, so AB is perpendicular to the plane. Hence A is the mirror image of B. Statement-1 is true. Statement-2 is true because the plane passes through the midpoint, but it does not mention the perpendicular condition, so it is not a complete explanation.

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Step-by-step solution

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